Best Known (86−43, 86, s)-Nets in Base 3
(86−43, 86, 44)-Net over F3 — Constructive and digital
Digital (43, 86, 44)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (7, 28, 16)-net over F3, using
- net from sequence [i] based on digital (7, 15)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 7 and N(F) ≥ 16, using
- net from sequence [i] based on digital (7, 15)-sequence over F3, using
- digital (15, 58, 28)-net over F3, using
- net from sequence [i] based on digital (15, 27)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 15 and N(F) ≥ 28, using
- net from sequence [i] based on digital (15, 27)-sequence over F3, using
- digital (7, 28, 16)-net over F3, using
(86−43, 86, 56)-Net over F3 — Digital
Digital (43, 86, 56)-net over F3, using
- t-expansion [i] based on digital (40, 86, 56)-net over F3, using
- net from sequence [i] based on digital (40, 55)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 40 and N(F) ≥ 56, using
- net from sequence [i] based on digital (40, 55)-sequence over F3, using
(86−43, 86, 350)-Net in Base 3 — Upper bound on s
There is no (43, 86, 351)-net in base 3, because
- 1 times m-reduction [i] would yield (43, 85, 351)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 37249 340707 414358 831400 021880 662717 933463 > 385 [i]